Dynamics of confined molecules within porous materials is equally important as local structural order, and it is necessary to quantify it and to reveal the microscopic mechanisms ruling it for better control of adsorption applications. In this study, molecular dynamics simulations were carried out to investigate the translational and the rotational dynamics of methanol trapped into the flexible NH-MIL-53(Al) metal-organics framework (MOF). Indeed, atomistic simulation is nowadays a relevant tool to explore matter at the nanoscale. Very recently it has been shown that the NH-MIL-53(Al) MOF material was capable to undergo a reversible structural transition (breathing phenomenon) by combining adsorption and thermal stimuli. This flexibility can drastically affect the dynamics of confined molecules and therefore the successful conduct of adsorption applications such as gas storage and separation. Rotational and translational dynamics of confined methanol through nanoporous flexible NH-MIL-53(Al) MOF were then deeply investigated by exploring a broad range of dynamical properties to extract the molecular mechanisms ruling them. This study allowed us to shed light on the interplay of dynamics of confined fluids and flexibility of porous material and to highlight the physical insights in diffusion mechanisms of confined molecules. Anomalous translational diffusion was evidenced due to a dynamical heterogeneity caused by a combination of a localized dynamics at the subnanometric scale and translational jumps between nanodomains in a zigzag scheme between the hydroxide group of the NH-MIL-53(Al). Actually, the non-Fickian dynamics of methanol is the result of the specific host-guest interactions and the MOF flexibility involving the pore opening. Eventually, decoupling between both rotational and translational dynamics related to breaking in the Stokes-Einstein relation was highlighted.